in the notation of [1]}.
(The superscript indicates in which simplicial category we are forming the bar construction.)
Using that \(Re\)  is simplicial and commutes with colimits, and that there is a natural isomorphism \(Re \circ {{Y}}_c \cong \mathrm {D}c\)  for any cartesian space \(c \in {{C}\mathrm {art}}\)  (cf. Lemma REF ), we obtain a canonical isomorphism
\(Re \circ Q^p (F) \cong B^{\Delta {T}\mathrm {op}}(F, {{C}\mathrm {art}}, \mathrm {D})\,.\) 
